HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Far-field reflector problem and intersection of paraboloids

Abstract : In this article, we study the intersection (or union) of the convex hull of N confocal paraboloids (or ellipsoids) of revolution. This study is motivated by a Minkowski-type problem arising in geometric optics. We show that in each of the four cases, the combinatorics is given by the intersection of a power diagram with the unit sphere. We prove the complexity is O(N) for the intersection of paraboloids and Omega(N^2) for the intersection and the union of ellipsoids. We provide an algorithm to compute these intersections using the exact geometric computation paradigm. This algorithm is optimal in the case of the intersection of ellipsoids and is used to solve numerically the far-field reflector problem.
Complete list of metadata

Cited literature [15 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00952720
Contributor : Quentin Mérigot Connect in order to contact the contributor
Submitted on : Thursday, February 27, 2014 - 1:51:35 PM
Last modification on : Friday, January 21, 2022 - 3:09:45 AM
Long-term archiving on: : Tuesday, May 27, 2014 - 11:17:09 AM

Files

ot-reflector.pdf
Files produced by the author(s)

Identifiers

Citation

Pedro Machado Manhães de Castro, Quentin Mérigot, Boris Thibert. Far-field reflector problem and intersection of paraboloids. Numerische Mathematik, Springer Verlag, 2016, 134 (2), pp.389-411. ⟨10.1007/s00211-015-0780-z⟩. ⟨hal-00952720⟩

Share

Metrics

Record views

753

Files downloads

508